How this pumped hydro calculator works
Pumped storage hydropower (PSH) is a giant rechargeable battery made of two reservoirs at different heights. When electricity is cheap or abundant, pumps lift water to the upper reservoir; when it is needed, the water flows back down through turbines. What it stores is the gravitational potential energy of the water, so volume and height difference (head) count in equal measure.
The calculator takes the usable volume, gross head and machine ratings and computes:
- the ideal gravitational energy and the electricity actually delivered after hydraulic, turbine, generator and transformer losses;
- the electricity needed to pump the water back up, and hence the round-trip efficiency;
- discharge and charge hours at the turbine and pump power, and the flow rate;
- drawdown of the upper reservoir and an Olympic-pool comparison;
- arbitrage revenue, simple payback and levelized cost of storage (LCOS), with the number of cycles capped to what the charge and discharge times physically allow.
The formulas
ρ = 1,000 kg/m³, g = 9.81 m/s², V in m³, H in m, h_loss = hydraulic losses as a fraction of head (each way).
Worked example: a 300 MW, 8-hour plant
The defaults describe an upper reservoir holding 2.5 million m³ of usable water (1,000 Olympic pools), 400 m above the lower reservoir, with reversible units of 300 MW:
- ideal stored energy: 1,000 × 9.81 × 2.5×10⁶ × 400 / 3.6×10⁹ ≈ 2,725 MWh;
- with 3% hydraulic loss each way, a 92% turbine, 91% pump, 98.5% motor-generator and 99.5% transformer efficiency, it delivers 2,380 MWh and needs 3,150 MWh to refill, a round-trip efficiency of about 76%;
- that is 7.9 hours at full power and 10.5 hours of pumping; the 40-hectare upper reservoir drops by about 6 m, small relative to the head;
- each cubic metre is worth about 0.95 kWh of delivered electricity.
Buying at €45/MWh and selling at €110/MWh for 300 cycles a year earns an arbitrage margin of about €36 million. With €2,000/kW capex (€600 million) the simple payback is around 19 years, and the LCOS including charging energy (about €119/MWh) sits slightly above the selling price. That is normal. Real plants also earn capacity payments and grid-service revenue (reserves, frequency response, inertia, black start), which this simple arbitrage view excludes.
How to read the results
- Energy delivered per cycle is the usable storage capacity at the grid connection.
- Round-trip efficiency: every MWh delivered costs 1/RTE MWh of charging electricity. At 76% efficiency the price spread must exceed about 24% of the selling price just to cover the losses.
- Discharge time decides which services the plant can sell. Daily cycling needs 4–10 hours; weekly or seasonal shifting needs much more.
- Drawdown: if the water level falls a lot relative to head, the head at the end of discharge is lower, and so are power and efficiency.
- LCOS vs capital-only cost: the gap is what you pay for the energy that charges the plant.
Typical values
| Parameter | Typical range |
|---|---|
| Gross head | 100–800 m (best 300–700 m) |
| Round-trip efficiency | 70–82% |
| Discharge duration | 6–12 h (some > 20 h) |
| Unit size | 100–400 MW per reversible unit |
| Capex | 1,500–3,500 per kW |
| Design life | 50–100 years |
| Response time | ~1–2 minutes from standstill; seconds when spinning |
Well-known examples: Dinorwig (UK, ~1.7 GW, ~9 GWh, ~500 m head), Goldisthal (Germany, ~1.06 GW, ~8.5 GWh, ~300 m) and Bath County (USA, ~3 GW, one of the largest in the world).
Tips
- Head beats volume. Doubling the head doubles the energy for the same dam, tunnel diameter and water volume, which is why high-head sites are much cheaper per MWh.
- Look for existing reservoirs. Pairing an existing lake or a former mine pit with a new reservoir cuts cost and environmental impact.
- Size power and energy separately. Turbines set MW, reservoirs set MWh; adding volume is often cheap compared with adding machines.
- Variable-speed units can regulate power while pumping, earning more from grid services.
- Compare with other options using the LCOE calculator and convert units with the energy unit converter.
Limitations
The model uses a single mean head; real head varies as reservoirs fill and empty. Evaporation, seepage, environmental flow obligations, ramp limits and outages are not modelled. Revenue covers energy arbitrage at a flat price spread only, and the cycle count is capped by charge and discharge time but not by market reality; actual plants rarely complete a full cycle every day. Capital costs are highly site-specific, dominated by tunnels, dams and geology.
Method & assumptions
Stored energy: E = ρ · g · V · H (J) ÷ 3.6×10⁹ = MWh, with ρ = 1,000 kg/m³ and g = 9.81 m/s². Generating delivers E · (1 − hloss) · ηturbine · ηgenerator · ηtransformer; pumping needs E · (1 + hloss) ÷ (ηpump · ηmotor · ηtransformer). Round-trip efficiency = delivered ÷ pumped (typically 70–82%). Discharge hours = delivered MWh ÷ turbine MW. LCOS = (capex × CRF + fixed O&M + charging cost) ÷ annual MWh delivered.
Frequently asked questions
How much energy can pumped hydro store?
What is the round-trip efficiency of pumped hydro?
How long can a pumped hydro plant generate?
How much does pumped hydro storage cost?
Is pumped hydro better than batteries?
How much of the world's energy storage is pumped hydro?
Sources & references
- IEA — Hydropower Special Market Report (2021)
- International Hydropower Association — Pumped storage hydropower
- Blakers, A., Stocks, M., Lu, B., Cheng, C. (2021). A review of pumped hydro energy storage. Progress in Energy 3(2)
- Mongird, K. et al. (2020). Energy Storage Grand Challenge Cost and Performance Assessment. PNNL / US DOE
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